In the end, I was able to unstuck myself by using another computer to build the system and copy the closure over SSH. After that, local builds worked fine.
path '/nix/store/037ni430ab9p42cplg3r3nwzgapalj17-python3.13-gssapi-1.10.1' disappeared, removing from database...
[... and many more...]
path '/nix/store/06v5dnvy7xfij23qywdiv9ilv559ija6-svelte-language-server-0.17.31' was modified! expected hash 'sha256-aWii1cn4uJoeEFxRuLPwwyYLz3nhmBcVFXcXERmBAnk=', got 'sha256-bx+aASSKs/FmOkuwDgL44en4aUlwlP6FIMrJBxk8sLw='
copying path '/nix/store/06v5dnvy7xfij23qywdiv9ilv559ija6-svelte-language-server-0.17.31' from 'https://cache.nixos.org'..
[... and many more...]
In the end, not exactly sure what happened, but it seems that I got back into a usable state